Construction of ODE systems from time series data by a highly flexible modelling approach

In this paper, a down-to-earth approach to purely data-based modelling of unknown dynamical systems is presented. Starting from a classical, explicit ODE formulation y′ = f(t, y) of a dynamical system, a method determining the unknown right-hand side f(t, y) from some trajectory data yk(tj), possibly very sparse, is given. As illustrative examples, a semi-standard predator-prey model is reconstructed from a data set describing the population numbers of hares and lynxes over a period of twenty years [1], and a simple damped pendulum system with a highly non-linear right-hand side is recovered from some artificial but very sparse data [2]. AMS classification scheme numbers: 65L09, 37M10, 92C42, 92D25